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Let 𝑀𝑘(𝑛) be the space of Siegel modular forms of degree 𝑛 and even weight 𝑘. In this paper firstly a certain subspace Spez(𝑀𝑘(2𝑛)), the Spezialschar of 𝑀𝑘(2𝑛), is introduced. In the setting of the Siegel threefold, it is proven that this Spezialschar is the Maass Spezialschar. Secondly, an embedding of 𝑀𝑘(2) into a direct sum ⨁⌊𝑘/10⌋𝜐=0 Sym2𝑀𝑘+2𝜐 is given. This leads to a basic characterization of the Spezialschar property. The results of this paper are directly related to the nonvanishing of certain special values of L-functions related to the Gross-Prasad conjecture. This is illustrated by a significant example in the paper.